Set Expressions (with Chainable Format) for Arithmetic and Relational Operations

I've been working with SetVar in choco-Solver. Unlike other types of variables, such as RealVar or IntVar, there was no direct way to compose operations such as equals (eq), not equals (ne), contains, not contains (nc), subset (subSet), union, or intersection directly in the model definition. While propagators allow for constructing such constraints, it was not as intuitive as it is for other variable types like IntVar and RealVar. These features are extremely useful in facilitating the composition of constraints.

Thus, I've worked on adding this feature for SetVar, based on the operations already available for other variable types. For example:

realVar.eq(3).post();

However, such expressions were not possible for SetVar:

setVar.eq(1, 2, 3).post();  // Not available... until now!

Improvement

I've implemented a new expression framework for SetVar, allowing the use of familiar operations directly on set variables. This change introduces support for the following operations:

Relational Operations:

• eq (Equals): setA.eq(1, 2, 3) or setA.eq(setB).
• ne (Not Equals): setA.ne(1, 2) or setA.ne(setB).
• contains: setA.contains(1, 2).
• nc (notContains): setA.notContains(1, 2).
• subSet: setA.subSet(1, 2, 3) or setA.subSet(setB).

Arithmetic Set Operations:

union: setA.union(setB)
intersection: setA.intersection(setB)

This enhancement allows for the expression of complex set relations with simplified syntax, enabling combinations such as:

setA.eq(setB.union(setC.intersection(setD))).post();

Example Usage:

Model model = new Model();

// Define set variables
SetVarImplArExpression setA = new SetVarImplArExpression(model, "setA", new int[]{}, new int[]{0, 1, 2, 3});
SetVarImplArExpression setB = new SetVarImplArExpression(model, "setB", new int[]{}, new int[]{1, 2, 3});
SetVarImplArExpression setC = new SetVarImplArExpression(model, "setC", new int[]{}, new int[]{2, 3, 4, 5});

// Compose set expressions
setA.eq(setB.union(setC)).post();
model.getSolver().propagate();

// Assert the expected values in setA
assertTrue(Arrays.equals(setA.getUB().toArray(), new int[]{1, 2, 3, 4, 5}));

Internal Changes:

This change is implemented through three main components:

• Unary Set Expressions (UnReSetExpression): Handle relations between a set and a list of values, like setVar.eq(1,2,3).post().
• Binary Set Expressions (BiReSetExpression): Manage operations between two SetVar instances, such as setA.eq(setB).post().
• Binary Arithmetic Expressions (BiArSetExpression): Handle arithmetic operations like unions and intersections, e.g., setA.eq(setB.union(setC)).post().

A new interface, SetExpression, inspired by other Choco-Solver expressions, allows SetVarExpression to be used in conjunction with these expression composition objects (UnReSetExpression, BiReSetExpression, and BiArSetExpression).

Backward Compatibility:

This improvement is fully backward-compatible with existing constraints and models. It adds considerable flexibility when working with SetVar, and I believe it will make modeling with sets much more intuitive.

Future Improvements:

I believe that additional operations, such as disjoint, could also be implemented to further enhance set operations in Choco-Solver.

Finally, I've included a comprehensive suite of tests in SetVarExpressionTest, which I hope will be useful to validate this enhancement.

I would greatly appreciate any feedback or suggestions for optimizations, as well as any edge cases that could further improve this approach!